No, your understanding of little-endian is incorrect. Little endian means that the least significant byte is at the lowest memory address.
Also:
As i understand it a dword equaling 0x11223344 on little endian systems will look like this:
0000 1011 0001 0110 0010 0001 0010 1100
That bit pattern doesn't have anything to do with 0x11223344
at all, be it little or big endian. On a little endian architecture, it would read
0100 0100 0011 0011 0010 0010 0001 0001
On a big endian system, however, the same would be
0001 0001 0010 0010 0011 0011 0100 0100